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• Other demands meant he was unable to commit fully

• Mike Yardy will step in for upcoming Pakistan fixture

Andrew Flintoff has decided to step down as the head coach of England Lions with immediate effect before his winter spell working in Australia’s Big Bash League (BBL).

The former all-rounder, 48, has been in charge of England’s second string since September 2024 and had been given the all-clear to leave this winter’s Lions tour of South Africa early to take up his new role at BBL side Sydney Thunder.

Scientists race to untangle complex links between exposure and mortality as fire weather grows more prevalent

A thousand kilometres from the infernos gorging on northern Ontario’s boreal forests, Erin O’Connor watched the sky above Canada’s biggest city turn an “almost post-apocalyptic” orange as it filled with light-scattering particles of soot and ash. Stepping outside the halls of Toronto General hospital, where air filters were keeping patients safe from the worst of the fumes, she was struck by a smell so strong it felt like standing by a campfire.

“It really hit you in the face as soon as you walked outside,” said O’Connor, who runs University Health Network’s emergency department and saw a rise in patients presenting with allergies and shortness of breath. “As the days progressed, it was like that everywhere. It seemed even inside you could smell that burning.”

With its sweet, caramelised edge and soft, creamy apple centre, you’ll be thinking about this cake for months after the first bite

For better or for worse (definitely for worse), this column is one-way. If we could talk, I’d ask you about the most mindblowing things you’ve eaten in your wild and precious life (feel free to use the comments). This year, for me, it was chef Lili’s apple cake at her restaurant, Limmat in Marseille. I’ve never had anything like it: a cake of pure apple – one and a half kilos – sliced and bound together with a breath of flour, a trickle of cream, a spoonful of sugar, a couple of eggs and a lot of time (in the oven). The result is a caramelised edge and a heavenly, scoopable, custard-like apple centre. Heavenly.

From running red lights to dumping bikes, some Lime users get a bad rap. But many who grumble about them don’t appreciate their own privilege

The night belongs to Lime bikes in the capital this summer. Buses and tube carriages are boiling, cars crawl between low traffic neighbourhoods and Thames Water roadworks, and pedestrians plod through the sticky heat. But Lime riders exist in a different, breezier realm: whirring along, chatting in pairs or blissfully alone, weaving through the city’s tree-lined maze, choosing impulsively between destinations, rarely stopping for anything or anyone.

“My favourite part of a night out is Lime biking home,” writes Annie Lord, a dating columnist and author, in Freewheeling: Essays on Cycling. “As I ride up a hill, the bike’s electrics click … And, for a little while, I’m free.”

Andy Beckett is a Guardian columnist

Authorities wrestle with fallout from mass border crossing, as tense Spanish enclave fears it will happen again

Along the wide avenues and tree-lined plazas of Ceuta’s centre, there were few hints of the recent events that catapulted the Spanish enclave on the north African coast into global headlines.

But less than a mile away from the bustling bars and restaurants, at the nearby El Trampolín beach, the lingering impact was impossible to ignore.

Some believe conflict strengthened national unity, others say it deepened repression, but all mourn the dead

The excavator stops suddenly. One of the workers reaches into the rubble and pulls something free. It isn’t twisted metal or broken concrete. It’s a child’s exercise book. The pages are still intact, covered in neat handwriting. On the front is a name: Mahya Salari. She was eight years old.

Five months after a missile tore through Shajareh Tayyebeh primary school in Minab, southern Iran, excavators are still clearing the site. Workers search for the remains of one young boy still believed to be buried beneath the debris.

Island’s government says no approval given after Greenland Energy brings kit ashore for exploratory drilling

An American oil company connected to Donald Trump is preparing to sink wells in remote Greenland despite not having received permission from the local authorities.

As the US president renews his threats to claim the vast Arctic territory, materials to prepare for drilling were brought ashore in recent days on Greenland’s eastern coast.

Scientists race to untangle complex links between exposure and mortality as fire weather grows more prevalent

A thousand kilometres from the infernos gorging on northern Ontario’s boreal forests, Erin O’Connor watched the sky above Canada’s biggest city turn an “almost post-apocalyptic” orange as it filled with light-scattering particles of soot and ash. Stepping outside the halls of Toronto General hospital, where air filters were keeping patients safe from the worst of the fumes, she was struck by a smell so strong it felt like standing by a campfire.

“It really hit you in the face as soon as you walked outside,” said O’Connor, who runs University Health Network’s emergency department and saw a rise in patients presenting with allergies and shortness of breath. “As the days progressed, it was like that everywhere. It seemed even inside you could smell that burning.”

Imogen, 31, a doctor, meets Andy, 36, founder of a consultancy firm

What were you hoping for?
Something to tell the group chat that would elicit more :o reactions than usual.

At 22, Ramsey has already been on our screens for a decade, and nominated for every award going. So why do they find it strange to be called an actor?

Bella Ramsey often feels more comfortable around older people. The actor, 22, who is non-binary and uses they/them pronouns, has been working professionally since they were 11, when they got their first TV job as the child noblewoman Lyanna Mormont in Game of Thrones. For half of their life, they have been in adult environments, talking to adults, working with adults. Even so, the London cafe in which Ramsey has chosen to meet makes any retirement home look like a creche. It is full of old men with their dogs, popping in for a cup of tea and a morning chat.

“It feels like it belongs in the Midlands. It feels a bit, like, shit and familiar,” says Ramsey, who grew up in the East Midlands and can say that with affection. Their curly hair is short, pushed back off their face, and they have a single gold hoop in one ear. The plan had been to go for a walk this morning, but it is raining so we have a cup of tea and wait for the drizzle to pass. Ramsey seems both younger and older than 22, depending on the moment. Sometimes, within a single sentence, they sound ancient and wise, and also like a bookish teenager, discovering with amazement how they think they might feel about the world.

Trump ally Abelardo De La ‌Espriella vows to start ‘profound transformation’ of country’s destiny as he is sworn in

The ​Trump administration plans to provide $1bn in security assistance to the ⁠government of Colombia’s new ​rightwing ‌president, the US state department announced, soon after Abelardo De La ‌Espriella was sworn in and used his inaugural speech to pledge a vigorous fight against drug trafficking, as well as austerity measures to restore confidence in the economy.

De La Espriella, 48, won June’s runoff election with ⁠promises to crack down on armed groups, shrink ⁠the state by as much as 40% and ​revive the oil and gas sector.

British and Germans themselves share stereotype but other nationalities are likelier to put out towels – or umbrellas

Germans are sunlounger hoggers, or so the longstanding stereotype goes. But not only is that cultural trope mostly confined to British – and, even more so, German – perceptions, surprising new data reveals that in fact Italian and French holidaymakers are the ones most likely to use their towel to stake their claim to a sunlounger.

A poll by YouGov of Europeans holidaymakers found that while many Germans (51%) and Britons (46%) associate Germans with the ritual of waking up at the crack of dawn to mark their spot, the perception barely exists elsewhere in Europe, with just 5-17% of those surveyed in other countries sharing the stereotype.

Trump ally Abelardo De La ‌Espriella vows to start ‘profound transformation’ of country’s destiny as he is sworn in

The ​Trump administration plans to provide $1bn in security assistance to the ⁠government of Colombia’s new ​rightwing ‌president, the US state department announced, soon after Abelardo De La ‌Espriella was sworn in and used his inaugural speech to pledge a vigorous fight against drug trafficking, as well as austerity measures to restore confidence in the economy.

De La Espriella, 48, won June’s runoff election with ⁠promises to crack down on armed groups, shrink ⁠the state by as much as 40% and ​revive the oil and gas sector.

British and Germans themselves share stereotype but other nationalities are likelier to put out towels – or umbrellas

Germans are sunlounger hoggers, or so the longstanding stereotype goes. But not only is that cultural trope mostly confined to British – and, even more so, German – perceptions, surprising new data reveals that in fact Italian and French holidaymakers are the ones most likely to use their towel to stake their claim to a sunlounger.

A poll by YouGov of Europeans holidaymakers found that while many Germans (51%) and Britons (46%) associate Germans with the ritual of waking up at the crack of dawn to mark their spot, the perception barely exists elsewhere in Europe, with just 5-17% of those surveyed in other countries sharing the stereotype.

В естественном языке распространена ситуация, когда значение слова нельзя установить без контекста: «замок закрыли ключом», «замок окружён рвом».

С позиции здравого смысла кажется, что у каждой отдельной вещи должно быть своё отдельное имя, но, как видно на практике, в этом нет необходимости.

В языке существует способ упаковать несколько значений в одно слово-омоним. В этой работе мы сознательно отказываемся от однозначности слов. Будет представлен алгоритм, сжимающий словарь русского языка в десятки и сотни раз, используя раскраску графа.

Мы рассмотрим, насколько естественные языки поддаются такому сжатию, и посмотрим, как выглядят языки с максимальным числом омонимов.

The race between Susan Collins and Troy Jackson is one of the nation's most high-profile Senate contests this year -- and may ultimately be decided by an especially powerful voting bloc: Maine women.

Depot hit in city of Ekaterinburg and hundreds evacuated in latest attack on Russian online retail giant. What we know on day 1,625

Officials describe ‘deplorable conditions’ at home run by pair linked to crematory closed due to mishandled remains

The remains of 56 people were found improperly stored and decomposing on Thursday at a Chicago funeral home run by a couple who previously operated a crematory that was similarly shut down because of mishandled remains, authorities said.

Illinois state officials, meanwhile, suspended the license of one of the funeral home’s directors, alleging bodies were being kept in an unrefrigerated area in “deplorable conditions”.

Обычно событие представляют линейно, нечто произошло, вызвало определённые последствия и стало частью прошлого. Подобное описание позволяет установить хронологическую последовательность, но не раскрывает внутреннюю структуру события. Оно фиксирует только реализованный факт и оставляет за пределами рассмотрения те возможности, которые существовали до его наступления, а также новые вероятностные продолжения, возникшие после него.

Событие нельзя полностью свести к отдельному факту, расположенному на временной шкале. Оно одновременно связано с предшествующим состоянием, моментом перехода и полем возможных последствий. В нём соединяются действительное, возможное и контрфактическое. Благодаря этому событие приобретает не только причинное, но и смысловое значение [1].

Под событийной сингулярностью понимается особая точка, в которой фактически произошедшее, множество возможных траекторий и возникшее следствие образуют единую динамическую структуру. Речь идёт не о физической сингулярности и не о технологическом скачке. Сингулярность здесь обозначает уникальный момент изменения, после которого прежняя конфигурация возможностей уже не сохраняется в неизменном виде.

Событие в таком понимании не просто происходит внутри некоторой системы. Оно перестраивает саму структуру её возможного продолжения.

Внутренняя событийность

У события можно выделить внешнюю и внутреннюю стороны. Внешняя сторона представляет собой наблюдаемый факт: действие совершено, решение принято, состояние изменилось. Внутренняя событийность охватывает отношения между тем, что произошло, тем, что могло произойти, и тем, что стало возможным после факта.